Parameter estimation for dynamic microbial inactivation: which model, which precision?

Dynamic Thermal Treatments in Green Coconut Water Induce Dynamic Stress Adaptation of Listeria innocua That Increases Its Thermal Resistance

The global coconut water market is projected to grow in the upcoming years, attributed to its numerous health benefits. However, due to its susceptibility to microbial contamination and the limitations of non-thermal decontamination methods, thermal treatments remain the primary approach to ensure the shelf-life stability and the microbiological safety of the product. In this study, the thermal inactivation of Listeria innocua, a Listeria monocytogenes surrogate, was evaluated in coconut water and in tryptone soy broth (TSB) under both isothermal (50-60 °C) and dynamic conditions (from 30 to 60 °C, with temperature increases of 0.5, 1 and 5 °C/min). Mathematical models were used to analyse the inactivation data. The Geeraerd model effectively described the thermal inactivation of L. innocua in both TSB and coconut water under isothermal conditions, with close agreement between experimental data and model fits. Parameter estimates and analysis revealed that acidified TSB is a suitable surrogate medium for studying the thermal inactivation of L. innocua in coconut water, despite minor differences observed in the shoulder length of inactivation curves, likely attributed to the media composition. The models fitted to the data obtained at isothermal conditions fail to predict L. innocua responses under dynamic conditions. This is attributed to the stress acclimation phenomenon that takes place under dynamic conditions, where bacterial cells adapt to initial sub-lethal treatment stages, leading to increased thermal resistance. Fitting the Bigelow model directly to dynamic data with fixed z-values reveals a three-fold increase in D-values with lower heating rates, supporting the role of stress acclimation. The findings of this study aid in designing pasteurization treatments targeting L. innocua in coconut water and enable the establishment of safe, mild heat treatments for refrigerated, high-quality coconut water.

Disentangling the contributions of initial heterogeneities and dynamic stress adaptation to nonlinearities in bacterial survival curves

The deviations from log-linearity that are often observed in bacterial survivor curves can be explained using different arguments, both biological and experimental. In this study, we used Bacillus subtilis as a model organism to demonstrate that the generally accepted vitalistic arguments (initial heterogeneities in the stress resistance of the cells in the population) may fail to describe microbial inactivation in some situations. In this sense, we showed how dynamic stress acclimation during an isothermal treatment provides an alternative explanation for survivor curves with an upwards curvature. We also provided an innovative experimental approach based on preadaptation experiments to evaluate which hypothesis is more suitable for the bacterial response. Furthermore, we used our experimental results to define bounds for the possible stress acclimation that may take place during dynamic treatments, concluding that the magnitude of stress acclimation may be larger for dynamic treatments than for isothermal experiments. We also evaluated the contribution of the SigB general stress response system to heat resistance by comparing the heat survival of wt and the ΔsigB mutant. Both strains survived better in 51, 52.5 and 55 °C when cells were pre-adapted at 48 °C than non-pre-adapted cells. However, ΔsigB was less resistant to heat than wt due to the missing SigB general stress system. Although these conclusions were based on B. subtilis as a model organism, this study can be the first step towards the development of a novel methodology able to estimate dynamic effects using only isothermal experiments. This would improve the models developed within the predictive microbiology community, improving our ability to predict microbial inactivation during industrial treatments, which are most often dynamic.

Drastic Microbial Count Reduction in Soy Milk Using Continuous Short-Wave Ultraviolet Treatments in a Tubular Annular Thin Film UV-C Reactor

Vegetative cells of Listeria monocytogenes and Escherichia coli and spores of Bacillus subtilis and Aspergillus niger were inoculated in soy milk at an initial concentration of ≈5 log CFU/mL. Inoculated and control (non-inoculated) soy milk samples were submitted to three types of treatments using a tubular annular thin film short-wave ultraviolet (UV-C) reactor with 1 mm of layer thickness. Treatments applied depended on the flow rate and the number of entries to the reactor, with UV-C doses ranging from 20 to 160 J/mL. The number of entries into the reactor tube (NET) was established as the most determining parameter for the efficiency of the UV-C treatments. Conidiospores of A. niger were reported as the most resistant, followed by B. subtilis spores, while vegetative cells were the most sensible to UV-C, with Listeria monocytogenes being more sensible than Escherichia coli. Treatments of just 80 J/mL were needed to achieve a 5 log CFU/mL reduction of L. monocytogenes while 160 J/mL was necessary to achieve a similar reduction for A. niger spores.

Microbial decontamination assisted by ultrasound-based processing technologies in food and model systems: A review

Ultrasound (US) technology is recognized as one of the emerging technologies that arise from the current trends for improving nutritional and organoleptic properties while providing food safety. However, when applying the US alone, higher power and longer treatment times than conventional thermal treatments are needed to achieve a comparable level of microbial inactivation. This results in risks, damaging food products' composition, structure, or sensory properties, and can lead to higher processing costs. Therefore, the US has often been investigated in combination with other approaches, like heating at mild temperatures and/or treatments at elevated pressure, use of antimicrobial substances, or other emerging technologies (e.g., high-pressure processing, pulsed electric fields, nonthermal plasma, or microwaves). A combination of US with different approaches has been reported to be less energy and time consuming. This manuscript aims to provide a broad review of the microbial inactivation efficacy of US technology in different food matrices and model systems. In particular, emphasis is given to the US in combination with the two most industrially viable physical processes, that is, heating at mild temperatures and/or treatments at elevated pressure, resulting in techniques known as thermosonication, manosonication, and manothermosonication. The available literature is reviewed, and critically discussed, and potential research gaps are identified. Additionally, discussions on the US's inactivation mechanisms and lethal effects are included. Finally, mathematical modeling approaches of microbial inactivation kinetics due to US-based processing technologies are also outlined. Overall, this review focuses only on the uses of the US and its combinations with other processes relevant to microbial food decontamination.

Predictive Microbial Modeling of Enterococcus faecium NRRL B-2354 Inactivation during Baking of a Multicomponent Low-Moisture Food

ABSTRACT

The use of baking ovens as a microbial kill step should be validated based on results of thermal inactivation models. Although traditional isothermal models may not be appropriate for these dynamic processes, they are being used by the food industry. Previous research indicates that the impact of additional process conditions, such as humidity, should be considered when validating thermal processes for the control of microbial hazards in low-moisture foods. In this study, the predictive performance of traditional and modified thermal inactivation kinetic models accounting for process humidity were assessed for predicting inactivation of Enterococcus faecium NRRL B-2354 in a multi-ingredient composite food during baking. Ingredients (milk powder, protein powder, peanut butter, and whole wheat flour) were individually inoculated to achieve ∼6 log CFU/g, equilibrated to a water activity of 0.25, and then mixed to form a cookie dough. An isothermal inactivation study was conducted for the dough to obtain traditional D- and z-values (n = 63). In a separate experiment, cookies were baked under four dynamic heating conditions: 135°C, high humidity; 135°C, low humidity; 150°C, high humidity; and 150°C, low humidity. Process humidity measurements; time-temperature profiles for the product core, surface, and bulk air; and microbial survivor ratios were collected for the four conditions at six residence times (n = 144). The traditional isothermal model had a high root mean square error (RMSE) of 856.51 log CFU/g, significantly overpredicting bacterial inactivation during the process. The modified model accounting for the dynamic time-temperature profile and process humidity data was a better predictor with an RMSE of 0.55 log CFU/g. These results indicate the importance of accounting for additional process parameters in baking inactivation models and that model performance can be improved by utilizing model parameters obtained directly from industrial-scale experimental data.

HIGHLIGHTS

On optimum dynamic temperature profiles for thermal inactivation kinetics determination

Determination of inactivation kinetics, associated with thermal processing of foods and obtained from dynamic temperature experiments, requires carefully designed experiments, the primary element being the selection of the appropriate temperature profile along with a carefully planned sampling schedule. In the present work, a number of different dynamic temperature profiles were investigated in terms of their ability to generate accurate kinetic parameters with low confidence intervals (CIs). Although alternative models have been also tested, our work was concentrated on thermal inactivation kinetics that could be described by the classical D-z values. A pair of D and z values was assumed, and for each temperature profile tested, concentration data at different processing times were generated through the appropriate models. Next, an error (up to ±2.5% or ±5%) was introduced on these theoretical values to generate pseudo-experimental data, and the back-calculation of the assumed kinetic parameters by non-linear regression was performed. The accuracy and the 95% CIs of the estimated kinetic parameters were evaluated; joint confidence regions were also constructed to investigate parameters correlation. The effect of temperature profile pattern, level of error, number of experimental points, and reference temperature was assessed. A stepwise increasing and a single triangle-pattern temperature profile were the best profiles among those tested. As a general observation, based on different kinetic models investigated, temperature profiles and sampling intervals that result in concentration versus time diagrams having shapes as suggested by the primary model used when isothermally applied are not considered appropriate for parameter estimation.

Dynamic modelling of Legionella pneumophila thermal inactivation in water

A predictive mathematical model describing the effect of temperature on the inactivation of Legionella pneumophila in water was developed. Thermal inactivation of L. pneumophila was monitored under isothermal conditions (51 - 61°C). A primary log-linear model was fitted to the inactivation data and the estimated D values ranged from 0.23 to 25.31 min for water temperatures from 61 to 51°C, respectively. The effect of temperature on L. pneumophila inactivation was described using a secondary model, and the model parameters z value and D_ref (D-value at 55°C) were estimated at 5.54°C and 3.47 min, respectively. The developed model was further validated under dynamic temperature conditions mimicking various conditions of water thermal disinfection in plumbing systems. The results indicated that the model can satisfactorily predict thermal inactivation of the pathogen at dynamic temperature environments and effectively translate water temperature profiles to cell number reduction. The application of the model in combination with effective temperature monitoring could provide the basis of an integrated preventive approach for the effective control of L. pneumophila in plumbing systems.

Dynamic kinetic analysis of growth of Listeria monocytogenes in pasteurized cow milk

The objective of this study was to develop a dynamic model for predicting the growth of Listeria monocytogenes in pasteurized cow milk under fluctuating temperature conditions during storage and temperature abuse. Six dynamic temperature profiles that simulated random fluctuation patterns were designed to change arbitrarily between 4 and 30°C. The growth data collected from 3 independent temperature profiles were used to determine the kinetic parameters and construct a growth model combining the primary and secondary models using a 1-step dynamic analysis method. The results showed that the estimated minimum growth temperature and maximum cell concentration were 0.6 ± 0.2°C and 7.8 ± 0.1 log cfu/mL (mean ± standard error), with the root mean square error (RMSE) only 0.3 log cfu/mL for model development. The model and the associated kinetic parameters were validated using the data collected under both dynamic and isothermal conditions, which were not used for model development, to verify the accuracy of prediction. The RMSE of prediction was approximately 0.3 log cfu/mL for fluctuating temperature profiles, and it was between 0.2 and 1.1 log cfu/mL under certain isothermal temperatures (2-30°C). The resulting model and kinetic parameters were further validated using 3 growth curves at 4, 7, and 10°C arbitrarily selected from ComBase (www.combase.cc). The RMSE of prediction was 0.8, 0.4, and 0.5 log cfu/mL, respectively, for these curves. The validation results indicated the predictive model was reasonably accurate, with relatively small RMSE. The model was then used to simulate the growth of L. monocytogenes under a variety of continuous and square-wave temperature profiles to demonstrate its potential application. The results of this study showed that the model developed in this study can be used to predict the growth of L. monocytogenes in contaminated milk during storage.

Thermal inactivation kinetics of Salmonella and Enterococcus faecium NRRL B-2354 on dried basil leaves

The enhanced heat resistance of Salmonella developed at low water activity makes it a serious challenge to eliminate them during thermal processing. The objectives of this research are to (i) investigate the effect of water activity on thermal inactivation of Salmonella cocktail (Agona, Tennessee, Mbandaka, Montevideo, and Reading) in dried basil leaves, and (ii) evaluate Enterococcus faecium NRRL B-2354 as an appropriate surrogate for Salmonella in dried basil leaves. Dried basil leaves, inoculated with a Salmonella cocktail and E. faecium separately, were equilibrated to different water activities (a_w: 0.40, 0.55, and 0.70) in a humidity-controlled chamber. The basil samples were packed (1.6 ± 0.1 g) in aluminum pouches and thermally treated at 70, 75, and 80 °C using a dry heating method for 0-180 min to obtain the thermal death curve. The microbial survival data was fit using two primary models (Log-linear and Weibull model). Results from AIC_c showed that the log-linear model fits well for thermal inactivation of both microorganisms. As the a_w decreases from 0.70 to 0.40 at 75 °C, the D-value increases from 3.30 to 9.14 min for Salmonella and 6.53 to 14.07 min for E. faecium. Based on the AIC_c values, the modified Bigelow model fits the D-values better than the response surface model for both the microorganisms. The kill ratio of surrogate to pathogen ranged from 1.4 to 2.8, indicating that it is a conservative surrogate for Salmonella for performing validation of the thermal pasteurization process. The identification of suitable surrogate and development of modified Bigelow model will help the spice industry in developing the thermal processes for improving the safety of basil leaves.

Variability in the heat resistance of Listeria monocytogenes under dynamic conditions can be more relevant than that evidenced by isothermal treatments

Heterogeneity in the response of microbial cells to environmental conditions is inherent to every biological system and can be very relevant for food safety, potentially being as important as intrinsic and extrinsic factors. However, previous studies analyzing variability in the microbial response to thermal treatments were limited to data obtained under isothermal conditions, whereas in the reality, environmental conditions are dynamic. In this article we analyse both empirically and through mathematical modelling the variability in the microbial response to thermal treatments under isothermal and dynamic conditions. Heat resistance was studied for four strains of Listeria monocytogenes (Scott A, CECT 4031, CECT 4032 and 12MOB052), in three different matrices (buffered peptone water, pH 7 Mcllvaine buffer and semi-skimmed milk). Under isothermal conditions, between-strain and between-media variability had no impact in the heat resistance, whereas it was very relevant for dynamic conditions. Therefore, the differences observed under dynamic conditions can be attributed to the variability in the ability for developing stress acclimation. The highest acclimation was observed in strain CECT 4031 (10-fold increase of the D-value), while the lowest acclimation was observed in strain CECT 4032 (50% increase of the D-value). Concerning the different media, acclimation was higher in buffered peptone water and semi-skimmed milk than in Mcllvaine buffer of pH 7.0. To the knowledge of the authors, this is the first research work that specifically analyses the variability of microbial adaptation processes that take place under dynamic conditions. It highlights that microbial heat resistance under dynamic conditions are sometimes determined by mechanisms that cannot be observed when cells are treated in isothermal conditions (e.g. acclimation) and can also be affected by variability. Consequently, empirical evidence on variability gathered under isothermal conditions should be extrapolated with care for dynamic conditions.

Effect of water activity on the thermal inactivation kinetics of Salmonella in milk powders

Persistence of Salmonella in milk powders has caused several foodborne outbreaks. The determination of proper pasteurization processing conditions requires an understanding of the thermal inactivation kinetics of Salmonella in milk powders. However, there is a lack of knowledge related to the effects of water activity (a_w) and fat content on Salmonella inactivation in milk powder during thermal processing. Two types of milk powders, nonfat dry milk and whole milk powder, with different fat contents (0.62 and 29.46% wt/wt, respectively) were inoculated with a 5-strain cocktail of Salmonella and equilibrated to 3 a_w levels (0.10, 0.20, and 0.30) for isothermal treatments at 75, 80, and 85°C to obtain D-values (the time required to achieve a 10-fold reduction of the bacteria at the isothermal treatment temperature) and z-values (the increase in temperature required to achieve a 90% reduction of the decimal reduction time D). Stability tests showed that the inoculation method used in this study provided a high and stable population of Salmonella for thermal inactivation studies. A moisture sorption isotherm was measured to understand the relationship between a_w and moisture content of milk powders. The thermal resistance of Salmonella was found to significantly increase as a_w decreased, which suggested that a higher temperature or longer processing time would be required at low a_w to achieve the desired inactivation of Salmonella. The microbial inactivation kinetics were not significantly different for the 2 milk powders; therefore, data were combined to develop a universal model. A response surface model was compared with a modified Bigelow model. The modified Bigelow model performed well to predict D-values [root mean square error (RMSE) = 1.47 min] and log reductions (RMSE = 0.48 log cfu/g). The modified Bigelow model developed here could be used to estimate D-value as a function of water activity and temperature to design a thermal pasteurization system for milk powders.

Limonene nanoemulsified with soya lecithin reduces the intensity of non-isothermal treatments for inactivation of Listeria monocytogenes

Consumers' demands for ready-to-eat, fresh-like products are on the rise during the last years. This type of products have minimal processing conditions that can enable the survival and replication of pathogenic microorganisms. Among them, Listeria monocytogenes is of special concern, due to its relatively high mortality rate and its ability to replicate under refrigeration conditions. Previous research works have shown that nanoemulsified essential oils in combination with thermal treatments are effective for inactivating L. monocytogenes. However, previous research works were limited to isothermal conditions, whereas actual processing conditions in industry are dynamic. Under dynamic conditions, microorganism can respond unexpectedly to the thermal stress (e.g. adaptation, acclimation or increased sensitivity). In this work, we assess the combination of nanoemulsified D-limonene with thermal treatments under isothermal and dynamic conditions. The nanoemulsion was prepared following an innovative methodology using soya lecithin, a natural compound as well as the essential oil. Under isothermal heating conditions, the addition of the antimicrobial enables a reduction of the treatment time by a factor of 25. For time-varying treatments, dynamic effects were relevant. Treatments with a high heating rate (20 °C/min) are more effective than those with a slow heating rate (1 °C/min). This investigation demonstrates that the addition of nanoemulsified D-limonene can greatly reduce the intensity of the thermal treatments currently applied in the food industry. Hence, it can improve the product quality without impacting its safety.

Guidelines for the design of (optimal) isothermal inactivation experiments

Kinetic models are nowadays a basic tool to ensure food safety. Most models used in predictive microbiology have model parameters, whose precision is crucial to provide meaningful predictions. Kinetic parameters are usually estimated based on experimental data, where the experimental design can have a great impact on the precision of the estimates. In this sense, Optimal Experiment Design (OED) applies tools from optimization and information theory to identify the most informative experiment under a set of constrains (e.g. mathematical model, number of samples, etc). In this work, we develop a methodology for the design of optimal isothermal inactivation experiments. We consider the two dimensions of the design space (time and temperature), as well as a temperature-dependent maximum duration of the experiment. Functions for its application have been included in the bioOED R package. We identify design patterns that remain optimum regardless of the number of sampling points for three inactivation models (Bigelow, Mafart and Peleg) and three model microorganisms (Escherichia coli, Salmonella Senftenberg and Bacillus coagulans). Samples at extreme temperatures and close to the maximum duration of the experiment are the most informative. Moreover, the Mafart and Peleg models require some samples at intermediate time points due to the non-linearity of the survivor curve. The impact of the reference temperature on the precision of the parameter estimates is also analysed. Based on numerical simulations we recommend fixing it to the mean of the maximum and minimum temperatures used for the experiments. The article ends with a discussion presenting guidelines for the design of isothermal inactivation experiments. They combine these optimum results based on information theory with several practical limitations related to isothermal inactivation experiments. The application of these guidelines would reduce the experimental burden required to characterize thermal inactivation.

Coupling the dynamics of diffused gases and microbial growth in modified atmosphere packaging

Coupling microbial dynamics with the complete dynamics of the packaging gases is still a challenge. In this work the microbial growth kinetic parameters for Pseudomonas and Lactic Acid Bacteria (LAB) in MAP are identified based on accurate estimation of diffusivity of gases and parameter scaled sensitivity approaches. The microbial dynamics are also compared with those estimated based on partial pressure measurement. Scaled sensitivity coefficient analysis using dissolved gases as variable inputs, shows that in most cases the only coefficients large enough for estimation were those for CO_2max-diss, and for μ_max. The current data showed that dissolved gases led significant differences on the microbial parameter of CO_2max values when compared with the headspace gases. On the other hand, the (so-called) dissolved specific growth rate follows a clear trend down for both microorganisms in relation to the increase of the initial headspace CO₂. Finally, current results indicate a possible correlation between CO_2max-diss, CO_{2max-headspace}, and μ_max as functions of CO_2init.

Relevance of the Induced Stress Resistance When Identifying the Critical Microorganism for Microbial Risk Assessment

Decisions regarding microbial risk assessment usually have to be carried out with incomplete information. This is due to the large number of possible scenarios and the lack of specific data for the problem considered. Consequently, risk assessment studies are based on the information obtained with a small number of bacterial cells which are considered the most heat resistant and/or more capable of multiplying during storage. The identification of the most resistant strains is usually based on D and z-values, normally estimated from isothermal experiments. This procedure omits the potential effect that the shape of the dynamic thermal profile applied in industry has on the microbial inactivation. One example of such effects is stress acclimation, which is related to a physiological response of the cells during sub-lethal treatments that increases their resistance. In this article, we use a recently published mathematical model to compare the development of thermal resistance for Escherichia coli K12 MG1655 and E. coli CECT 515 using inactivation data already published for these strains. Based only on the isothermal experiments, E. coli K12 MG1655 would be identified as more resistant to the thermal treatment than the CECT 515 strain in the 50-65°C temperature range. However, we conclude that stress acclimation is strain (and/or media)-dependent; the CECT 515 strain has a higher capacity for developing a stress acclimation than K12 MG1655 (300% increase of the D-value for CECT 515, 50% for K12 MG1655). It, thus, has the potential to be more resistant to the thermal treatment than the K12 MG1655 strain for some conditions allowing acclimation. A methodology is proposed to identify for which conditions this may be the case. After calibrating the model parameters representing acclimation using real experimental data, the applicability of the proposed approach is demonstrated using numerical simulations, showing how the CECT 515 strain can be more resistant for some heating profiles. Consequently, the most resistant bacterial strain to a dynamic heating profile should not be identified based only on isothermal experiments (D- and z-value). The relevance of stress acclimation for the treatment studied should also be evaluated.

Mathematical quantification of the induced stress resistance of microbial populations during non-isothermal stresses

This contribution presents a mathematical model to describe non-isothermal microbial inactivation processes taking into account the acclimation of the microbial cell to thermal stress. The model extends the log-linear inactivation model including a variable and model parameters quantifying the induced thermal resistance. The model has been tested on cells of Escherichia coli against two families of non-isothermal profiles with different constant heating rates. One of the families was composed of monophasic profiles, consisting of a non-isothermal heating stage from 35 to 70°C; the other family was composed of biphasic profiles, consisting of a non-isothermal heating stage followed by a holding period at constant temperature of 57.5°C. Lower heating rates resulted in a higher thermal resistance of the bacterial population. This was reflected in a higher D-value. The parameter estimation was performed in two steps. Firstly, the D and z-values were estimated from the isothermal experiments. Next, the parameters describing the acclimation were estimated using one of the biphasic profiles. This set of parameters was able to describe the remaining experimental data. Finally, a methodology for the construction of diagrams illustrating the magnitude of the induced thermal resistance is presented. The methodology has been illustrated by building it for a biphasic temperature profile with a linear heating phase and a holding phase. This diagram provides a visualization of how the shape of the temperature profile (heating rate and holding temperature) affects the acclimation of the cell to the thermal stress. This diagram can be used for the design of inactivation treatments by industry taking into account the acclimation of the cell to the thermal stress.

Modeling the Effect of Temperature and Water Activity on the Thermal Resistance of Salmonella Enteritidis PT 30 in Wheat Flour

Salmonella continues to be a problem associated with low-moisture foods, particularly given enhanced thermal resistance at lower water activity (a_w). However, there is a scarcity of thermal inactivation models accounting for the effect of a_w. The objective of this study was to test multiple secondary models for the effect of product (wheat flour) a_w on Salmonella enterica Enteritidis phage type 30 thermal resistance. A full-factorial experimental design included three temperatures (75, 80, and 85°C) and four a_w values (~0.30, 0.45, 0.60, and 0.70). Prior to isothermal treatment, sample a_w was achieved by equilibrating samples in a humidity-controlled conditioning chamber. Two primary models (log linear and Weibull type) and three secondary models (second-order response surface, modified Bigelow type, and combined effects) were evaluated using the corrected Akaike information criterion and root mean squared errors. Statistical analyses of the primary models favored the log-linear model. Incorporating the three secondary models into the log-linear primary model yielded root mean squared errors of 2.1, 0.78, and 0.96 log CFU/g and corrected Akaike information criterion values of 460, -145, and -19 for the response surface, modified Bigelow, and combined-effects models, respectively. The modified Bigelow-type model, which exponentially scaled both temperature and a_w effects on thermal inactivation rates, predicted Salmonella lethality significantly better (P < 0.05) than did the other secondary models examined. Overall, a_w is a critical factor affecting thermal inactivation of Salmonella in low-moisture products and should be appropriately included in thermal inactivation models for these types of systems.

One-step global parameter estimation of kinetic inactivation parameters for Bacillus sporothermodurans spores under static and dynamic thermal processes

Bacillus sporothermodurans produces highly heat-resistant endospores, that can survive under ultra-high temperature. High heat-resistant sporeforming bacteria are one of the main causes for spoilage and safety of low-acid foods. They can be used as indicators or surrogates to establish the minimum requirements for heat processes, but it is necessary to understand their thermal inactivation kinetics. The aim of the present work was to study the inactivation kinetics under both static and dynamic conditions in a vegetable soup. Ordinary least squares one-step regression and sequential procedures were applied for estimating these parameters. Results showed that multiple dynamic heating profiles, when analyzed simultaneously, can be used to accurately estimate the kinetic parameters while significantly reducing estimation errors and data collection.

Use of simulation tools to illustrate the effect of data management practices for low and negative plate counts on the estimated parameters of microbial reduction models

In the last 20 years, the use of microbial reduction models has expanded significantly, including inactivation (linear and nonlinear), survival, and transfer models. However, a major constraint for model development is the impossibility to directly quantify the number of viable microorganisms below the limit of detection (LOD) for a given study. Different approaches have been used to manage this challenge, including ignoring negative plate counts, using statistical estimations, or applying data transformations. Our objective was to illustrate and quantify the effect of negative plate count data management approaches on parameter estimation for microbial reduction models. Because it is impossible to obtain accurate plate counts below the LOD, we performed simulated experiments to generate synthetic data for both log-linear and Weibull-type microbial reductions. We then applied five different, previously reported data management practices and fit log-linear and Weibull models to the resulting data. The results indicated a significant effect (α = 0.05) of the data management practices on the estimated model parameters and performance indicators. For example, when the negative plate counts were replaced by the LOD for log-linear data sets, the slope of the subsequent log-linear model was, on average, 22% smaller than for the original data, the resulting model underpredicted lethality by up to 2.0 log, and the Weibull model was erroneously selected as the most likely correct model for those data. The results demonstrate that it is important to explicitly report LODs and related data management protocols, which can significantly affect model results, interpretation, and utility. Ultimately, we recommend using only the positive plate counts to estimate model parameters for microbial reduction curves and avoiding any data value substitutions or transformations when managing negative plate counts to yield the most accurate model parameters.